Digital images represent visual information as a spatial array of sampled intensity, color, or other spectral information. Sampling is typically done on a regular grid, such as a hexagonal grid pattern, or most commonly, a rectangular or square grid pattern. To avoid creating digital aliasing artifacts, the sampling must obey the Nyquist criterion, i.e., the image is typically blurred or filtered prior to sampling such that the highest spatial frequencies present complete no more than one cycle for every two samples.
For various reasons, a digital image may be blurred to a much larger extent than that required by Nyquist. The optics that focused the image may be imperfect or out of focus, or the subject or optics may have moved during sampling. The image may be band-limited due to lossy compression, or filtered to reduce transmission bandwidth. In such cases, it may be desirable to run an edge-sharpening filter to “restore” lost high-frequency content prior to image display. In other cases, an edge-sharpening filter could be used simply to create an aesthetically pleasing effect on an otherwise focused and full-bandwidth image.
Many researchers have proposed methods for sharpening image edges. Linear filtering methods include unsharp masking, which creates a derivative image of high-spatial frequency regions on an image, and then adds the derivative image to the original. Such methods are discussed in G. Ramponi and A. Polesel, “A Rational Unsharp Masking Technique”, Journal of Electronic Imaging, vol. 7, no. 2, Apr. 1998, pp. 333-38. Unfortunately, like real edges, noise also has high-spatial frequency, and thus unsharp masking tends to enhance image noise. Unsharp masking can also produce overshoot and undershoot near image edges.
Deblurring can also be done using deconvolution filtering. Such methods attempt to invert the blurring process by processing the image with an inverse estimate of the blurring function. Such solutions are also susceptible to noise, and can have stability problems.
Other researchers have proposed non-linear methods for sharpening image edges. One such approach is “shock filters”, as described in U.S. Pat. No. 5,644,513, “System Incorporating Feature-Oriented Signal Enhancement Using Shock Filters”, issued to L. Rudin and S. Osher. The shock filter is an iterative “diffusion” process that uses partial differential equations and relies on locating the image edge nearest each pixel, and that edge's orientation. Once that edge is identified, the pixel is adjusted to be more like its neighbor or neighbors that are further away from the edge. Through successive iterations, image edges become sharper as more pixels become like the pixels away from the edges. Because this method relies on locating edges, e.g., through locating zero-crossing points in a second derivative image, its success is also limited by noise that can fool an edge detector, as well as by the effectiveness of the edge detector in locating actual edges. Further, numerical stability must be balanced against convergence speed, and it may be difficult to determine how many iterations should be performed.